Privacy in the Strategic Provision of Performance Feedback: Theory and
3.5. RESULTS 93 Table 3.5: Feedback to Both Agents in Private Feedback
Private-Verifiable (message) Private-Unverifiable (message)
Actual Both Info Info,No Info No Info, Info Both No Info SS SF FS FF No-No SNo NoS FNo NoF
SS 5 0 0 0 6 0 0 0 0 0 0 0 0
(100.00) (0.00) (0.00) (0.00) (100.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
SF 7 4 1 0 7 1 0 0 0 1 0 0 0
(58.33) (33.33) (8.33) (0.00) (77.78) (11.11) (0.00) (0.00) (0.00) (11.11) (0.00) (0.00) (0.00)
FS 5 0 5 0 4 0 5 0 0 2 0 0 0
(50.00) (0.00) (50.00) (0.00) (36.36) (0.00) (45.45) (0.00) (0.00) (18.18) (0.00) (0.00) (0.00)
FF 4 1 0 9 5 1 0 5 1 1 2 0 0
(28.57) (7.14) (0.00) (64.29) (33.33) (6.67) (0.00) (33.33) (6.67) (6.67) (13.33) (0.00) (0.00) Number of agents receiving each message type, percentages in parentheses
The abbreviations in message part represents message pairs.
S= Successful, F= Failed and No= No message. SNo refers to (Successful, No message) message pair.
Table 3.6: Feedback to Both Agents in Public Feedback
Public-Verifiable (message) Public-Unverifiable (message)
Actual Both Info Both No Info SS SF FS FF No-No SNo NoS FNo NoF
SS 8 0 3 0 0 0 0 0 1 0 0
(100.00) (0.00) (75.00) (0.00) (0.00) (0.00) (0.00) (0.00) (25.00) (0.00) (0.00)
SF 6 3 4 3 0 1 0 4 0 0 1
(66.67) (33.33) (30.77) (23.08) (0.00) (7.69) (0.00) (30.77) (0.00) (0.00) (7.69)
FS 9 4 7 1 3 0 0 1 1 0 0
(69.23) (30.77) (53.85) (7.69) (23.08) (0.00) (0.00) (7.69) (7.69) (0.00) (0.00)
FF 5 6 1 0 0 1 5 0 0 0 0
(45.45) (54.55) (14.29) (0.00) (0.00) (14.29) (71.43) (0.00) (0.00) (0.00) (0.00) Number of agents receiving each message type, percentages in parentheses
The abbreviations in message part represents message pairs.
S= Successful, F= Failed and No= No message. SNo refers to (Successful, No message) message pair.
Our design also allows us to observe the expectations of the principals regard-ing how agents will update their beliefs. This can potentially give insights into the rationale behind the principals’ strategy. As shown in Figure 3.4, principals ex-pect the positive feedback they send to be interpreted more optimistically than it actually is (although this is not significant in a Wilcoxon test), and negative mes-sages to be evaluated significantly more pessimistically (p = 0.003 in a Wilcoxon test). Thus, principals generally overestimate the response of agents’ beliefs to the feedback, especially when the feedback is negative. The expectation of a pes-simistic response to negative feedback reveals that at least some principals take into account its adverse effect on beliefs but provide negative feedback anyway, which is consistent with an aversion to lying.
Figure 3.4: Difference between Principal’s Guess and Actual Belief
11.0
−3.2
4.4
−50510Difference between guess and belief
Negative Feedback Positive Feedback No Feedback
Finally, we examine principals’ expectations regarding how agents’ beliefs will be influenced by the feedback given to the other agent. As Table 3.7 shows, prin-cipals expect that a positive feedback to the other agent will adversely influence the beliefs of an agent when his own feedback is also positive and when feedback is public and unverifiable, but expect no significant impact if own feedback is neg-ative or feedback is verifiable.27 Interestingly, this is a feature of the equilibrium of the model with lying costs and naive agents, which will be analyzed in Section 3.6.
Table 3.7: Principal’s Expectations in Public Feedback-Extended
Own Positive Feedback Own Negative Feedback
(1) (2) (3) (4) (5) (6)
Guess Guess Guess Guess Guess Guess
(Public-Verifiable) (Public-Unverifiable) (Public-Verifiable) (Public-Unverifiable)
Other Positive Feedback -3.151 3.708 -10.195∗∗ -1.550 -0.333 -3.323
(3.198) (5.692) (4.176) (8.969) (7.903) (17.649)
Public-Verifiable 10.188∗∗∗ 4.722
(2.960) (3.169)
N 75 31 44 37 25 12
χ2 14.735 0.424 5.959 2.250 0.002 0.035
Standard errors in parentheses
GLS Regressions for Different Feedback Mechanisms
∗p < .1,∗∗p < .05,∗∗∗p < .01
We can summarize our findings as follows.
27Note, however, that the number of observations is small in some of these regressions.
3.6. DISCUSSION 95 Result 3.5. Some principals prefer to tell the truth even when they know that this might adversely affect their payoff. Prediction 1.4 is confirmed but 2.3 is rejected.
3.6 Discussion
Overall, our theoretical model in Section 3.4 does a good job in terms of ex-plaining the relative informativeness of different feedback mechanisms. There are, however, three major discrepancies between our theoretical predictions and em-pirical findings: (1) Some principals report truthfully even when they believe that this may hurt them; (2) Agents do not interpret “no feedback” as pessimistically as the theory suggests; (3) Positive feedback is interpreted less optimistically if the other agent also receives positive feedback and this effect is stronger in public-unverifiable than in public-verifiable feedback.
The finding that some principals have a tendency to tell the truth is in line with previous empirical studies of strategic communication and suggests that individu-als suffer from cost of lying and this cost varies among them. The second finding might be due to naiveté in belief formation, i.e., agents interpret the feedback literally and when they receive “no information”, they keep their priors more or less unchanged. Another finding that supports the naive agent hypothesis is that, even in private-verifiable feedback, a significant fraction of principals provide no information when the agent has failed. Since “no information” and negative feed-back must both be interpreted in the same (pessimistic) way in private-verifiable feedback, this is not rational if there is even a minimal preference for telling the truth. If, however, principals believe that some of the agents are naive, then this may be optimal. Indeed, Figure 3.4 and the preceding discussion have indicated that principals expect agents to respond to feedback in a somewhat naive way.
Therefore, we conclude that at least some agents are naive and that principals expect them to act naively. The third finding could be due to the fact that agents make (non-Bayesian) social comparisons in forming their beliefs or they believe
that the difficulty of the tasks are correlated in such a way that if the other agent has succeeded, then probability of own success in the next task is smaller.
Another possible explanation of this finding is that agents are rational and such beliefs simply follow from the principals’ strategy and Bayes’ rule.
In the next section we extend our theoretical model to allow for individual-specific cost of lying (and cost of withholding information) for the principals and naiveté on the part of the agents. We will see that such an extension can account for most of our empirical findings as well as some of the above discrepancies between the predictions of the original model and the data.
3.6.1 Cost of Lying and Naive Agents
Suppose that lying or providing no information has an individual specific cost associated with it. Let c(r|θ) be the cost of sending report r when the state is θ and assume that it is distributed according to the probability distribution Fr|θ in the population. Also assume that (1) telling the truth is costless; (2) there are some individuals for whom the cost of lying is small; (3) there are some who always prefer to tell the truth; (4) there are some for whom the difference between the cost of lying and cost of withholding information is small enough; and (5) there are some who prefer withholding information to lying.28
A fraction η ∈ (0, 1) of agents are naive, i.e., they believe that the state is exactly equal to the principal’s report and if the report is “no information”, then they keep their prior unchanged. Let qi(r|θ)denote the fraction of principals with type θ who send report r to agent i in private feedback, and q(r|θ) denote the same fraction in public feedback.
Before we present our results, we should briefly discuss the few existing theo-retical studies of cheap talk games with lying costs and naive agents. Kartik et al.
28These assumptions are equivalent to the following: (1) Fθ|θ(x) = 1 for all x ≥ 0;
(2) Fr|θ(x) > 0 for all r, θ and x > 0; (3) Fr|θ(v(a1(1), a2(1), θ) − v(a1(0), a2(0), θ) <
1; (4) c(s, r−i|f, θ−i) − c(∅, r−i|f, θ−i) is a non-negative random variable with probability distribution G (.|r−i, θ−i) such that G (x|r−i, θ−i) > 0 for all r−i, θ−i and x > 0; (5) G (v(ai(1), a−i(µ−i(r−i)), f, θ−i) − v(ai(0), a−i(µ−i(r−i)), f, θ−i)|r−i, θ−i) < 1for all r−i, θ−i.
3.6. DISCUSSION 97